I would not assume cooling has been worked out. Space is a vacuum. i.e. The lack-of-a-thing that makes a thermos great at keeping your drink hot. A satellite is, if nothing else, a fantastic thermos. A data center in space would necessarily rely completely on cooling by radiation, unlike a terrestrial data center that can make use of convection and conduction. You can't just pipe heat out into the atmosphere or build…
At earth or above sea, we use cooling to maintain the temperature below 60 degrees, or 80 or 100 or something.
Shadow of space is -157 degrees, the cooling design will be different.